A body is rolling without slipping on a horizontal surface and its rotational kinetic energy is equal to the translational kinetic energy. The body is 

1.  Disc

2.  Sphere

3.  Cylinder

4.  Ring

A wheel with a radius of 20 cm has forces applied to it as shown in the figure. The torque produced by the forces of 4 N at A, 8N at B, 6 N at C, and 9N at D, at the angles indicated, is:
                    
1.  5.4 N-m anticlockwise

2.  1.80 N-m clockwise

3.  2.0 N-m clockwise

4.  3.6 N-m clockwise

The moment of inertia of a thin rectangular plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is 

1.  ${\mathrm{I}}_1 + {\mathrm{I}}_2$

2.  ${\mathrm{I}}_2 + {\mathrm{I}}_4$

3.  ${\mathrm{I}}_1 - {\mathrm{I}}_3$

4.  ${\mathrm{I}}_1 + {\mathrm{I}}_{2 }+ {\mathrm{I}}_3 + {\mathrm{I}}_4$

The centre of a wheel rolling on a plane surface moves with a speed \(v_0.\) A particle on the rim of the wheel at the same level as the centre will be moving at speed:
1. zero
2. \(v_0\)
3. \(\sqrt{2}v_0\)
4. \(2v_0\)

Moment of inertia of a uniform cylinder of mass M, radius R and length l about an axis passing through its center and normal to its axis would be

1.  $\frac{{\mathrm{Ml}}^2}{12}$

2.  $\frac{{\mathrm{MR}}^2}{2}$

3.  $\mathrm{M}\left[\frac{{\mathrm{l}}^2}{12} + \frac{{\mathrm{R}}^2}{4}\right]$

4.  $\mathrm{M}\left[\frac{{\mathrm{l}}^2}{12} + \frac{{\mathrm{R}}^2}{2}\right]$

A particle moves along a circle of radius $\frac{20}{\mathrm{\pi }}m$ with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begin, the tangential acceleration is

1. 640 $\mathrm{\pi } \mathrm{m}/{\mathrm{s}}^2$

2. 160 $\mathrm{\pi } \mathrm{m}/{\mathrm{s}}^2$

3. 40 $\mathrm{\pi } \mathrm{m}/{\mathrm{s}}^2$

4. 40 $\mathrm{m}/{\mathrm{s}}^2$

If the radius of the earth is suddenly contracted to half of its present value, then the duration of the day will be of:

A wheel has angular acceleration of 3.0 rad/$se{c}^2$ and an initial angular speed of 2.00 rad/sec.  In a time of 2 sec it has rotated through an angle (in radian) of 

1. 10               

2. 12

3. 4                 

4. 6

If a force acts on a body at a point away from the centre of mass, then 

1.  Linear acceleration changes 

2.  Angular acceleration changes 

3.  Both change 

4.  None of these

If the linear density of a rod of length \(3 \text m\) varies as $$\(\lambda= \text{2+x} \), then the position of the center of mass of the rod is at a distance of:
1. \({7 \over 3}m\)
2. \({10 \over 7}m\)
3. \({12\over 7}m\)
4. \({9 \over 7}m\)